To find the area that the goat can graze, we need to determine the area of the sector formed by the rope.
The length of the rope is 7m, which is the radius of the sector.
The angle formed by the sector can be found using the formula:
[ \text{angle} = \frac{{\text{length of rope}}}{{\text{radius}}} = \frac{7}{7} = 1 ]
Next, we can find the area of the sector using the formula:
[ \text{Area of sector} = \frac{{\text{angle}}}{{360}} \times \pi \times \text{radius}^2 ]
Substituting the given values:
[ \text{Area of sector} = \frac{1}{360} \times \pi \times 7^2 ]
Simplifying, we get:
[ \text{Area of sector} = \frac{1}{360} \times 49\pi ]
[ \text{Area of sector} \approx 0.135\pi ]
To find the area that the goat can graze, we subtract the area of the sector from the area of the square plot:
[ \text{Area grazed} = \text{Area of square plot} - \text{Area of sector} ]
[ \text{Area grazed} = 12^2 - 0.135\pi ]
[ \text{Area grazed} \approx 144 - 0.135\pi ]
Now we need to approximate the value of (\pi). Taking (\pi) as 3.14 (rounded to two decimal places), we can calculate the area grazed:
[ \text{Area grazed} \approx 144 - 0.135 \times 3.14 ]
[ \text{Area grazed} \approx 144 - 0.4249 ]
[ \text{Area grazed} \approx 143.5751 ]
Therefore, the area that the goat can graze is approximately 143.5751 square meters.
Since none of the given options match the calculated area, we can conclude that the correct answer is D) None of these.